Basement Insulation/Building Science

Hi

The infamous "diaper"that's in my basement, well I can't find who manufactured it.
It goes to 6 inches above the floor, as explained.

I am planning to have half my basement unfinished storage, and leave the existing insulation up. The finished area's walls will be about 1/2-1" from the poured concrete (or existing diaper insulation depending on the answers below).

If the air space behind the finished space is contiguous to the unfinsihed basement:
1) Is it still better to rip down the diaper?
2) Does the fact that the wall ends remain "open" help any moisture/airflow problems or will it not matter?

Basement Insulation/Building Science

It seems to say diaper insulation is "ok" but better with a 6" gap at the bottom for moisture diffusion.

Also, maybe I'm nuts for leaving air cycle behind the walls...that is to say have the storage/unfinished areas abutt the finished space.
Yes, a 1/2-1" isn't much space for air to travel, but shouldn't it let moisture diffuse?